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For me, intuitively the answer seems to be yes. But I don't know how this could be justified a priori. The hypothesis "x does not exist" seems not to be simpler than the hypothesis "x exists". By the principle of indifference, both options should therefore be assumed to be equally likely. But this doesn't seem right to me.

The question also could be equivalent to this one:

Is it, a priori, more likely that the complexity of the universe is smaller than larger?

Because a universe where less exists is presumably less complex and vice versa.

Max
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    How unknown is the object? If nothing is know at all this becomes is it more likely that there is something rather than nothing, and I'd say that it is overwhelmingly more likely that there is. And sorry, but I am missing why the boldface question is equivalent to the title one, or even how they are connected at all. – Conifold Sep 13 '17 at 23:07
  • @Conifold A universe where less exists is presumably less complex and vice versa. – Max Sep 14 '17 at 07:38
  • The connection you want to draw suffers from a pretty damning reductio that shows we shouldn't try to figure out whether the universe exists by looking just an a prior argument for the superiority of simplicity: taken to its extreme (and merely a priori), the assumption would seem to imply that nothing in the universe and moreover the universe itself does not exist (by repeated application of the assumption the simpler is more likely) – virmaior Sep 14 '17 at 11:24
  • @virmaior A priori likeliness doesn't necessarily imply truth. – Max Sep 14 '17 at 12:52
  • Does it imply anything at all? – virmaior Sep 14 '17 at 13:41
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    "Unknown" says it all: unknown. But if you are nitpicking, ask yourself what the word "likely" means. I do not know, but I think this seemingly trivial subject is huge. – George Chen Sep 14 '17 at 13:51
  • @virmaior Yes it does, namely how strongly you should expect something. Which in turn can influence your behavior. The principle of indifference (cited above) is an example for this. – Max Sep 14 '17 at 14:23
  • I don't see why it implies `how strongly you should expect something`. At best,1. it implies how strongly you should expect something in the total absence of empirical sense data of any kind (hence the *a priori*), but since 2. expectations are about things we sense ... 3. ??? 4. Profit! – virmaior Sep 14 '17 at 15:48
  • @virmaior I don't know what you mean. The principle of indifference is an a priori principle, just as Occam's razor and probably other principles. These principles tell you which possibility you should prefer, which means: how strongly you should expect something. – Max Sep 14 '17 at 16:00
  • Maybe I'm not following what you're proposing, but I read you as suggesting this. (1) assume an *a priori* principle of indifference and (2) assume an *a priori* principle of parsimony. Then you ask, if we make both assumptions, what happens? My answer: it would be most logical to assume *a priori* that NOTHING exists. But this would be absurd because *a posteriori* we know that something exists. Ergo, it's a mistake to assume both principles *a priori* because the logical outcome of this is absurd. – virmaior Sep 14 '17 at 16:20
  • Moreover, the principle of indifference tells you to assume equal probabilities, but the *a priori* is a realm where no events occur, so you're just left with percentages across an infinite chain of cascading possibilities -- which have no connection the world. – virmaior Sep 14 '17 at 16:22
  • That something is unlikely doesn't exclude the possibility that it is true. So I don't know what should be absurd here. You seem to further claim claim that _a priori_ justified beliefs have no effect on the world. But of course they have. Philosophy, especially analytic philosophy, is largely an a priori discipline. Even more so mathematics. They have great effect, they just do not derive their justification from empirical data. – Max Sep 14 '17 at 17:03
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    You will be hard pressed to find a philosopher today who believes in Kantian style justificatory a priori. The "a priori" recognized today are fallible presuppositions, loosely based on past experience, used to build hypothetical explanations and models. The order of justification is reversed, it is the a posteriori success of explanations that justifies the "a priori". If you start from blank slate then the principle of indifference will tell you that x existing and not are equiprobable, but unless you can use this to explain something it goes nowhere. – Conifold Sep 14 '17 at 20:01
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    pray tell, what on earth does "a priori an unknown object does not exist". can you see the problem? the propososal ("unknown object") already assumes what you're trying to establish. your question is perfectly meaningless. –  Sep 14 '17 at 20:23
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    i.e. "an unknown object" already tells us there must be such an object - otherwise it could not be an unknown object. –  Sep 14 '17 at 20:26
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    p.s. epistemology != ontology. and neither has anything to do with complexity. what does "small complexity" even mesn? –  Sep 14 '17 at 20:33
  • @Conifold Most philosophers believe that there is a priori knowledge or at least a priori justification, only a few (followers of Quine's "web of belief") do not. If you mean with "Kantian style" synthetic a priori knowledge you may well be right, but that's not the only form of a priori knowledge (not even for Kant), just look at analytic statements. The principle of indifference to which you refer is in fact believed by many to be justified a priori, e.g. because it is analytic. – Max Sep 15 '17 at 21:09
  • @mobileink If you think that something you don't know anything about can't exist you are a solipsist. Here is more information on the topic: https://plato.stanford.edu/entries/nonexistent-objects/ "Small complexity" means something like "little information needed for a description". You can find more explanation here: https://en.m.wikipedia.org/wiki/Kolmogorov_complexity If you have further questions you should ask them separately on stack exchange, this gets a little off topic here. – Max Sep 15 '17 at 21:11
  • @max: read harder. i never said that things we do not know cannot exist. –  Sep 15 '17 at 21:22
  • you cannot ascribe a property like "does not exist" to something that does not exist. indeed "something that does not exist" is preposterous. –  Sep 15 '17 at 21:35
  • @mobileink Then for you _every_ positive existence statement is true, because "x does not exist" is always false? Because sentences like "Stana Claus does not exist" are supposedly "preposterous"? What about hypothetical (non-)existence statements in science? Well that's a funny view, but doesn't get you very far. Just read the Standford Encyclopedia article on nonexistent objects I posted above. – Max Sep 16 '17 at 18:43
  • And of course existence doesn't have to be a property of an object, e.g. it can also be a fact of whether some singular term x corresponds to an object in the world or not, very similar to the correspondence theory of truth (which instead talks about a correspondence of propositions to facts). – Max Sep 16 '17 at 18:44
  • @Max: no. "Santa clause exists" is meaningful, but it has no truth value. Just like "Time is red." –  Sep 16 '17 at 18:54
  • @Max also note that the Principle of Indifference is not apriori. in fact it depends on underlying assumptions, which are optional. see https://plato.stanford.edu/entries/dialetheism/ –  Sep 16 '17 at 19:25
  • @mobileink Your view about existence statements is highly controversial which is a reason that you should not state it as a fact. Again, I refer to the article about nonexistent objects. Also you didn't answer my question about hypothetical existence statements which are perfectly common in science. According to your view, such a hypothesis is either true when the hypothetical object exists or neither true nor false otherwise. In the latter case probably every scientist would say the statement is false. You can call them what you like of course, but you risk then being misunderstood. – Max Sep 17 '17 at 15:50
  • As far as I can see the article on dialetheism does not say anything about the principle of indifference. In fact I don't know how you come to the idea that it is relevant here. You say that some statements are "neither true nor false" which amounts to a third truth value "gap" as it is used in the strong Kleene logic (system K3). But in dialetheism there are instead statements which are "both true and false" which amounts to a third truth value "glut" in Priests logic of paradox (system LP). These systems behave differently. So dialetheism is not even compatible with what you said before. – Max Sep 17 '17 at 16:03
  • You are correct that most believe in some form of analyticity, including late Quine, some even believe in synthetic a priori, see descriptions and references in [What are the more complex/interesting examples of synthetic a priori statements?](https://philosophy.stackexchange.com/a/37733/9148) But none of them provide a priori justification in the sense that would make your question meaningful. On all of these conceptions, except Kant's, analytic conventions and synthetic a priori can be discarded a posteriori if the explanations they furnish are deemed unsatisfactory. – Conifold Sep 17 '17 at 19:46
  • @Max: there is no controversy. some logics accept the Law of Exluded Middle, others don't. The principle of indifference does. if you reject LEM then the PoI is pointless. You can only assign probabilities to n possibilities if you accept LEM. –  Sep 17 '17 at 20:39
  • @Max: regarding scientists and "hypothetical existence statements": good scientists (imho) do not traffic in true/false. They worry about support, disconfirmation, etc. Newton's laws turned out to be false, meaning unsupportable. –  Sep 17 '17 at 20:48
  • If the object is "unknown", and we are to decide on the likeness of its existence upon the fact that it is unknown, we are no longer reasoning a priori. – Luís Henrique Jan 14 '18 at 02:38
  • just looking at what I expect the question to be maybe there is some subconscious observation of a large or infinite universe containing everything conceivable, or anything ever conceivable, respectively – TheAutomaton Feb 14 '18 at 18:23
  • I'm not sure, especially as I'm not much of an expert on the subject in any way, but maybe Occam's Razor is what the OP is looking for? The idea that the least assumptions made for a theory would make the theory "better" (or simply put - don't assume more than you need). – Yechiam Weiss Feb 14 '18 at 20:41
  • A bacon sandwich in the hand of some Chinese person: Totally unknown to me, but very very likely to exist. – gnasher729 Jul 05 '23 at 13:38

4 Answers4

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Before answering this question, one must ask what it means. What does it mean to calculate the probability that A exists? If it is unknown, should it even be given a non zero probability?

It seems to me that the only correct answer is to say that the question itself is vacuous and the answer doesn’t seem to map into reality in any meaningful way. For example, if I said that there is a 40% chance aliens exist. What does that mean?

If you take a frequentist approach, it’s clearly meaningless. We don’t have multiple “trials” or worlds where we can test whether or not 40% of them have aliens in them. If you take the subjective approach, which is how much of a belief you should have, you still deal with problems. How, or in what way, can you map your subjective credence into reality? If a person feels like there is a 40% probability that aliens exist, how does this translate into reality? And how does one determine their credence?

thinkingman
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Frequentist approach
Hypotheses x exist and x does not exist are complimentary: the object either exists or does not exist with probability 1 (i.e., 100%)

In research context, if trying to show existence of something, we would take x does not exist as the null hypothesis and x exists as the alternative hypothesis. We then would then collect data and estimate (using some model) the probability of the null hypothesis being true. Provided that this probability is lower than a priori significance threshold (which we agree upon before collecting the data), we would reject the null hypothesis.

Bayesian approach
In Bayesian approach probability is simply our belief in something, which we adjust according to the evidence available. The set of all the things actually existing can be thought of as a subset of all the things imaginable - that is, the subset of the actually existing this is "smaller". We could even strengthen the relation between these two sets by stating that to any actually existing object corresponds an infinite number of imagined ones. That is an arbitrary fruit of imagination, like the notorious Invisible Pink Unicorn are more likely not to exist than the other way around.

Roger Vadim
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Well the issue with the principle of indifference is that it only applies if there can be only one item in a set. For instance if you have 4 possibilities that all contradict each other, and thus only 1 can be true, you're looking at a situation where most are false, and it is most likely any one is false. However if you take 4 possibilities that do not contradict each other, and multiple can be true, it is also possible that most or even all of the possibilities are true, and thus you cannot say that it is unlikely for any particular one to be true.

Braydon
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  • But that's the point. We actually have here two contradicting possibilities, haven't we? "X exists" and "X doesn't exist" contradict each other for any X. – Max Sep 14 '17 at 07:42
  • That isn't really the meaning of this rule though, and given two possibilities you would only get that there is a 50% chance of something existing, which does not indicate it probably does not. – Braydon Sep 14 '17 at 12:59
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    But that's exactly what I was asking about: Can it really be rational to treat the hypothetical existence of some x as equally likely as it's hypothetical non-existence, as the principle of indifference seems to suggest? I don't know if you share this intuition, but to me it seems much more likely that an object, of which you do not know anything about whether it exists, does not exist than that it does. To put it in another way: Can it really be rational to expect the hypothetical existence of infinitely many unknown hypothetical objects with probably 50% each? – Max Sep 14 '17 at 14:37
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There are two contexts in which this question can be posed : (1) in your own case and (2) in the case of an agent without experience. 'Unknown' can mean 'unknown that it is' or 'known what it is'. I take it that both senses are implied.

1 If 'a priori' means 'prior to or independent of experience', then (I think) you cannot properly ask the question concerning yourself since you already have experience, and specifically experience of coming to know objects previously unknown in your experience. Inductively, but not a priori, this gives you good grounds for supposing that if you have encountered previously unknown objects in the past then you will also encounter them in future.

2 In the case of someone who has no experience of knowing any objects, I don't see how this person could have any idea of the probability or otherwise of there being unknown objects since no known object has been encountered. 'Unknown object' contrasts with 'known object' but ex hypothesi for this person there are no known objects to contrast with.

3 I think there is a general problem with a priori probability if we take a priori in anything like its standard sense (as above). Probability - likelihood - is probability on the evidence or given certain data :

P (A|B) - the probability of event A, given event B. But a priori, no events are or can be given or any relevant experience. So much is contained in the very idea of the a priori. So while it is interesting to speculate on the probability of there being unknown events, I don't think the a priori is the standpoint from which to approach the question.

Geoffrey Thomas
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